Interference Energy Spectrum of the Infinite Square Well
AbstractCertain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction
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Waegell, M.; Aharonov, Y.; Patti, T.L. Interference Energy Spectrum of the Infinite Square Well. Entropy 2016, 18, 149.
Waegell M, Aharonov Y, Patti TL. Interference Energy Spectrum of the Infinite Square Well. Entropy. 2016; 18(4):149.Chicago/Turabian Style
Waegell, Mordecai; Aharonov, Yakir; Patti, Taylor L. 2016. "Interference Energy Spectrum of the Infinite Square Well." Entropy 18, no. 4: 149.
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